2.1 Find roots (zeroes) of : F(x) = x3+5x2-18 Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integers
The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient
In this case, the Leading Coefficient is 1 and the Trailing Constant is -18.
The factor(s) are:
of the Leading Coefficient : 1 of the Trailing Constant : 1 ,2 ,3 ,6 ,9 ,18
The Factor Theorem states that if P/Q is root of a polynomial then this polynomial can be divided by q*x-p Note that q and p originate from P/Q reduced to its lowest terms
In our case this means that x3+5x2-18 can be divided with x+3
Polynomial Long Division :
2.2 Polynomial Long Division Dividing : x3+5x2-18 ("Dividend") By : x+3 ("Divisor")
The length of the rope in this case becomes the radius of the circle that the goat is able to graze. The area of the circle is calculated through the equation, A = πr² Substituting, A = π(5m)² = 78.54 m² Thus, the area that the goat is able to graze is equal to 78.54 m².